Global vs. Zonal Approaches in Hybrid

RANS-LES Turbulence Modelling

Florian. R. Menter1, Jochen Schütze

1 and Mikhail Gritskevich

2

1,ANSYS Germany GmbH,

2, NTS St. Petersburg

Abstract

The paper will provide an overview of hybrid RANS-LES methods currently

used in industrial flow simulations and will evaluate the models for a variety of

flow topologies. Special attention will be devoted to the aspect of global vs. zonal

approaches and aspects related to interfaces between RANS and LES zones.

Introduction

Historically, industrial CFD simulations are based on the Reynolds Averaged

Navier-Stokes Equations (RANS). For many decades, the only alternative to

RANS was Large Eddy Simulation (LES), which has however failed to provide

solutions for most flows of engineering relevance due to excessive computing

power requirements for wall-bounded flows. On the other hand, RANS models

have shown their strength essentially for wall-bounded flows, where the calibra-

tion according to the law-of-the-wall provides a sound foundation for further re-

finement. For free shear flows, the performance of RANS models is much less

uniform. For this reason, hybrid models are under development , where large ed-

dies are only resolved away from walls and the wall boundary layers are entirely

covered by a RANS model (e.g. Detached Eddy Simulation – DES or Scale-

Adaptive Simulation – SAS). A further step is the application of a RANS model

only in the innermost part of the wall boundary layer and then to switch to an LES

model for the main part of the boundary layer. Such models are termed Wall

Modelled LES (WMLES). Finally, for large domains, it is frequently only neces-

sary to cover a small portion with Scale-Resolving Simulation (SRS) models,

while the majority of the flow can be computed in RANS mode. In such situations,

zonal or embedded LES methods are attractive. Such methods are typically not

new models in the strict sense, but allow the combination of existing mod-

els/technologies in a flexible way in different zones of the simulation domain. Im-

portant elements of zonal models are interface conditions, which convert turbu-

lence from RANS mode to resolved mode at pre-defined locations. In most cases,

2

this is achieved by introducing synthetic turbulence based on the length and time

scales from the RANS model.

The challenge for the engineer is to select the most appropriate model for the

intended application. Unfortunately, none of the available SRS models is able to

efficiently cover all industrial flows. A compromise has to be made between gen-

erality and CPU requirements. The paper will discuss the main different models

available in today‟s industrial CFD codes and provide some guidelines as to their

optimal usage.

Hybrid RANS-LES Turbulence Models

There is a large variety of hybrid RANS-LES models with often somewhat

confusing naming conventions concerning the range of turbulence eddies they will

resolve. On close inspection, many of these models are slight variations of the De-

tached Eddy Simulation (DES) concept of Spalart (1997, 2000) with very similar

behavior. The present paper will provide a review of models which are in, or at the

verge of, industrial use – which reduces the model variety considerably. Naturally,

the authors will focus on the methods employed in our own CFD codes, and more

specifically ANSYS-Fluent and ANSYS-CFX. For a general overview of SRS

modelling concepts see e.g. Fröhlich and von Terzi (2008) or Sagaut et al. (2006).

It is not the goal of this paper to provide the full detail of all models, but to

highlight the main concepts and their consequences for the industrial usage.

Therefore only a schematic description of the models will be provided.

Scale-Adaptive Simulation (SAS)

SAS is a concept which enables Unsteady RANS (URANS) models to operate

in SRS mode. This is achieved by the introduction of the second derivative of the

velocity field into the turbulence scale equation. The derivation is based on a theo-

ry of Rotta (see e.g. Rotta, 1972), resulting in an exact equation for the turbulence

length scale. This equation served as a basis for a term-by-term modelling of the

length-scale equation. The details of the derivation and numerous examples can be

found in Menter and Egorov (2010), Egorov et al. (2010). The essential quantity,

which appears in the equations and which allows the switch to SRS mode is the

von Karman length scale Lvk:

2 2

2 2

' 1; '' ; ' 2 ;

'' 2

ji i ivK ij ij ij

k j j i

UU U UUL U U S S S S

U x x x x

Lvk allows the SAS model to detect resolved unsteady structures in the simula-

tion and to reduce the eddy-viscosity accordingly. Due to the lower eddy-

3

viscosity, new smaller structures can be generated resulting in a turbulence cas-

cade down to the grid limit. At the grid limit, different limiters can be employed

ensuring a proper dissipation of turbulence. The advantage of SAS models is that

the limiters do not affect the RANS behavior of the model.

Detached Eddy Simulation (DES)

Detached Eddy Simulation (DES) has been proposed by Spalart and co-

workers (Spalart et al., 1997, 2000, Travin et al., 2000, Strelets 2001), to eliminate

the main limitation of LES models, by proposing a hybrid formulation which

switches between RANS and LES based on the grid resolution provided. By this

formulation, the wall boundary layers are entirely covered by the RANS model

and the free shear flow portions are typically computed in LES mode. The formu-

lation is mathematically relatively simple and can be built on top of any RANS

turbulence model. DES has attained significant attention in the turbulence com-

munity as it allows the inclusion of SRS capabilities into every day engineering

flow simulations.

Within the DES model, the switch between RANS and LES is based on a crite-

rion like:

max; max , ,DES t x y z

DES t

C L RANS

C L LES

The actual formulation for a two-equation model is (e.g. k-):

As the grid is refined below the limit max tL the DES-limiter is activated and

switches the model from RANS to LES mode. The intention of the model is to run

in RANS mode for attached flow regions, and to switch to LES mode in detached

regions away from walls.

It is important to note that the DES limiter can already be activated by grid re-

finement inside attached boundary layers. This is undesirable as it affects the

RANS model by reducing the compute eddy viscosity which, in term, can lead

Grid-Induced Separation (GIS), as discussed by Menter et al. (2003) where the

boundary layers separates at arbitrary locations based on the grid spacing. In order

to avoid this, the DES concept has been extended to Delayed-DES (DDES), fol-

lowing the proposal of Menter et al. (2003) to „shield‟ the boundary layer from the

3/2

*t

k kL

3/2

max

( )( )( )

min ;

j tk

j t DES j j

U kk k kP

t x L C x x

4

DES limiter (Shur et al. 2008). The dissipation term in the k-equation is then re-

formulated as follows:

The function FDDES is formulated in such a way as to give FDDES=1 inside the

wall boundary layer and FDDES=0 away from the wall. The definition of this func-

tion is intricate as it involves a balance between save shielding and the desire to

not suppress the formation of resolved turbulence as the flow leaves the wall.

Wall Modelled Large Eddy Simulation (WMLES)

The motivation for WMLES is to reduce the Re number scaling of wall-

resolved LES. The principle idea is depicted in Figure 1. The near wall turbulence

scales with the wall distance, y,, resulting in smaller and smaller eddies as the wall

is approached. This effect is limited by viscosity, which damps out eddies inside

the viscous sublayer (VS). As the Re number increases, smaller and smaller eddies

appear, as the viscous sublayer becomes thinner. In order to avoid the resolution

of these small near wall scales, RANS and LES models are combined in a way,

where the RANS model covers the very near wall layer, and then switches over to

an LES formulation once the grid spacing is sufficient to resolve the local scales.

This is seen in Figure 1 bottom, where the RANS layer extends outside the VS and

avoids the need to resolve the second row of eddies depicted in the sketch.

Figure 1: Concept of WMLES for high Re number flows. Top:

Wall-resolved LES. Bottom: WMLES

3/2 3/2 3/2

max 1;min ; min 1;

tDES

t DES t DES t t DES

Lk k kE

L C L C L L C

max 1 , 1tDDES DDES

DES

LE F

C

5

The WMLES formulation used in ANSYS-CFD is based on the formulation of

Shur et al. (2008):

where again y is the wall distance, is the von Karman constant and S is the

strain rate. This formulation was adapted to suit the needs of the ANSYS general

purpose CFD codes. Near the wall, the min-function selects the Prandtl mixing

length model whereas away from walls it switches over to the Smagorinsky (1963)

model (with suitably defined cell size).

Figure 2 shows the results of a simulation of a boundary layer at Re=10000. Such

a Re number is typically out of reach for wall-resolved LES due to the large grid

resolution required. In the present study a grid with only ~1.3∙106 cells was used

(x+~700, z

+~350). Synthetic inlet turbulence was generated using the Vortex

Method (Mathey et al. 2003).The logarithmic layer is captured very well as seen

in Figure 2.

Figure 2: Profile information for the flat plate boundary layer

simulations. Re=10000.

Zonal/Embedded LES (ELES, ZLES)

The idea behind ZLES/ELES is to predefine different zones during the pre-

processing stage with different treatment of turbulence (e.g. Cokljat et al. 2009,

Menter et al. 2009). The domain is typically split into a RANS and a LES portion.

Between these regions, the turbulence model is switched from RANS to LES (or

WMLES). In order to maintain consistency, synthetic turbulence is generally in-

troduced at RANS-LES interfaces. ELES is actually not a new model, but an in-

frastructure which combines existing elements of technology in a zonal fashion.

The recommendations for each zone are therefore the same as given for the indi-

vidual models.

32 2min , 1 exp / 25t SMAGy C y S

6

Unsteady Inlet/Interface Turbulence

Classical LES requires providing unsteady fluctuations at turbulent in-

lets/interfaces (RANS-LES interface) to the LES domain. In the most general situ-

ation, the inlet profiles are not fully developed and no simple method exists of

producing consistent inlet profiles. In such cases, it is desirable to generate syn-

thetic turbulence based on given inlet profiles for RANS turbulence models. These

inlet profiles are typically obtained from a pre-cursor RANS simulation of the

domain upstream of the LES inlet. There are several methods for generating syn-

thetic turbulence. In ANSYS-Fluent, the most widely used method is the Vortex

Method (Mathey et al. 2003), where a number of discrete vortices are generated at

the inlet/interface. Their distribution, strength and size are modeled to provide the

desirable characteristics of real turbulence. The input parameters to the VM are

the two scales from the upstream RANS simulation. An alternative to the VM is

the generation of synthetic turbulence by using suitable harmonic functions used

in ANSYS-CFX (Menter et al. 2009).

Flow Types and Modelling

Globally Unstable Flows

The classical example of globally unstable flows are flows past bluff bodies.

Even when computed with a classical URANS model, will the simulation typically

provide an unsteady output.

From a physical standpoint, such flows are characterized by the formation of

„new‟ turbulence downstream of the body, whereby this turbulence is independent

from and effectively overrides the turbulence coming from the attached boundary

layers around the body. In other words, the turbulence in the attached boundary

layers has very little effect on the turbulence in the separated zone. The attached

boundary layers can, however, define the separation point/line on a smoothly

curved body and thereby affect the size of the separation zone.

Examples of globally unstable flows:

Flows past bluff bodies

Flows with strong swirl instabilities

Flows with strong flow interaction

Of all flows where SRS modelling is required, globally unstable flows are the

easiest to handle. They can typically be captured by a global RANS-LES model

like SAS or DDES, without the need for generating synthetic turbulence at pre-

7

defined interfaces or highly specialized grid generation procedures. Globally un-

stable flows are also the most beneficial for SRS, as experience shows that RANS

models often fail on such flows with large margins of error. Fortunately, a large

number of industrial flows fall into this category.

The safest SRS model for such flows is the SAS approach. It offers the ad-

vantage that the RANS model is not affected by the grid spacing and thereby

avoids all potential negative effects of (D)DES, like „grey zones‟ or grid induced

separation. The SAS concept reverts back to (U)RANS in case the mesh/time step

is not sufficient for LES and thereby preserves a strong „backbone‟ of modelling

independent of space and time resolution. SAS also avoids the need for shielding,

which for internal flows with multiple walls can suppress turbulence formation in

DDES models.

The alternative to SAS is DDES. If proper care is taken to ensure LES mesh

quality in the detached flow regions, the model is operating in its design environ-

ment, typically providing high quality solutions.

In many cases, the behavior of SAS and DDES is very similar. The reason for

recommending the SAS model lies in its safety due to the underlying RANS for-

mulation.

Figure 3 shows the flow around a triangular cylinder in crossflow(Sjunnesson,

1992) as computed with the SST-SAS and the SST-DDES models. It is important

to emphasize that the flow is computed with steady state boundary conditions (as

would be employed for a RANS simulation). Still, the flow downstream of the ob-

stacle turns quickly into unsteady (scale-resolving) mode, even though no unstead-

iness is introduced by any boundary or interface condition.

The Reynolds number based on freestream velocity and edge length is

Re=45,500 with an inlet velocity of 17.3 m/s. Periodic boundary conditions are

applied in spanwise direction. The simulations where run with ANSYS-Fluent us-

ing the BCD (bounded central difference, see e.g. Jasak et al. 1999)) and CD

(Central Difference) advection scheme and a time step of t=10-5

s (CFL~1 behind

cylinder).

The grid for the simulation around the triangular cylinder features 26 cells

across its base. It is extended in the third direction to cover 6 times the edge length

of the triangle with 81 cells in that direction. Due to the strong global instability of

this flow, such a resolution is sufficient and has produced highly accurate solu-

tions for mean flow and turbulence quantities. It should however be noted that not

all flows feature such a strong instability as the triangular cylinder, and a higher

grid resolution might then be required.

Figure 4 shows a comparison of results between SST-SAS, SST-DDES and ex-

perimental data. As can be seen, both models capture the flow well and agree with

the experiments.

8

Figure 3: Turbulence structures for flow around triangular

cylinder in crossflow.

Figure 4: Velocity profiles and turbulence RMS profiles for

three different stations downstream of the triangular cylinder

(x/a=0.375, x/a=1.53, x/a=3.75). Comparison of SST-SAS, SST-

DES models and experiment. (a: U-velocity, b: u’v’)

SST-SAS SST DDES

9

Locally Unstable Flows

The expression „locally‟ unstable flows is not easily definable as every turbu-

lent flow is unstable by nature. Still in lieu of a more suitable expression, we mean

here flows where a local shear layer generates an instability which turns the flow

into a fully turbulent flow within a small number of shear layer thicknesses

(<~3). To illustrate the rationale behind this definition, assume the computation

of a mixing layer starting from two wall boundary layers (Figure 5). As the flat

plate ends, the two boundary layers form a turbulent mixing layer, which becomes

relatively quickly independent from the turbulence of the two boundary layers on

the flat plate (yellow). The mixing layer instability (red) provides for a de-

coupling of the boundary layer and the mixing layer turbulence.

Figure 5: Generic Mixing length example for loclly unstable

flows

Examples of globally unstable flows:

All equilibrium free shear flows (jets, wakes, mixing layers).

Backward facing step flow

Weakly interacting equilibrium flows

Flows with weak swirl

The most general approach is the use of embedded or zonal RANS-LES meth-

ods, where the boundary layers are covered by a RANS model and the mixing lay-

er by a LES model. The models will explicitly be switched from RANS to LES at

a pre-defined interface. For a fully consistent simulation, one has to introduce syn-

thetic turbulence at the RANS-LES interface.

A similar effect to simply switching the turbulence model at the interface can

be achieved by the DDES model without an explicit interface between the RANS

and the LES zones. The shielding function will ensure that the wall boundary lay-

10

ers are not affected by the LES part of the model and are covered in RANS mode.

Slightly downstream of the trailing edge, the shielding function is deactivated and

the model operates in LES mode if the grid and time step are of LES-quality. The

model relies on the local instability of the mixing layer to produce the resolved

turbulence content. The dashed yellow turbulence sketched in Figure 5 down-

stream of the trailing edge is neglected by this approach.

SAS models will typically remain in RANS or URANS mode for such flows.

They should therefore not be used if unsteady flow characteristics are required.

However, interfaces can be provided similar to zonal or embedded LES, where

synthetic turbulence is introduced but the model is not switched. This then triggers

the SAS model into SRS mode.

The recommendation for flows with local instabilities is to use ELES/ZLES

models if the geometry and application allow the definition of well defined inter-

faces. One should introduce synthetic turbulence at these interfaces in order to

preserve the balance between the RANS and LES turbulence content. In case the

geometry/application is too complex and the definition of explicit RANS and LES

zones is not easily possible, the DDES model should be applied.

The backward-facing step flow of Vogel and Eaton (1985) has been computed

as an example using SST-DDES (see Gritskevich et al. (2011) for more details). In

this flow, the Reynolds number based on a bulk velocity and on the step height H

is equal to 28000, and the height of the channel upstream of the step is equal to

4H.

The computational domain, see Figure 6, in the present study extended from

-3.8H to 20H in streamwise direction (x=0 corresponds to the step location). In the

spanwise direction, the size of the domain was 4H.

The computational grid used in the simulation had 2.25 million hexahedral

cells (2.3 million nodes) providing a near-wall resolution in wall units to be less

than one. A non-dimensional time step was Δt=0.02 ensured the CFL number to

be less than one in the entire domain. The number of cells in the spanwise direc-

tion was 80. At the inlet condition, steady state RANS profiles were imposed and

unsteadiness results from the inherent flow instability past the step.

As seen in Figure 6, the skin friction distributions over the step-wall and ve-

locity fields agree well with the data. This indicates that the turbulence from the

upstream boundary layers (neglected in DDES past the step) is not essential for

capturing the downstream flow development. The flow instability of the mixing

layer is sufficiently quickly producing new turbulence to capture the main effects

in the separation and recovery zone.

11

Figure 6: A sketch of the flow (a) by SST-based DDES: b –skin

friction coefficient distribution over the step-wall, c and d –

profiles of streamwise velocity <u> and <u’u’> stress, e and f –

iso-surfaces of Q criterion equal to 1 [s-2]. Profiles are plotted at

x/H=2.2, 3.0, 3.7, 4.5, 5.2, 5.9, 6.7, 7.4, 8.7

Stable Flows

Flow Physics

Stable flows in this context are characterized by a continuous development of

the turbulence field. For such flows, the turbulence at a certain location depends

strongly on the turbulence upstream of it. There is no mechanism of quickly gen-

erating „new‟ turbulence and over-riding the upstream turbulence field. Stable

flows in the context of this discussion are essentially wall-bounded flows - either

attached or with small separation bubbles.

Channel and pipe flows (attached and mildly separated)

Boundary layers (attached and mildly separated)

For stable flows, the use of embedded or zonal RANS-LES methods with a

well defined interface between the RANS and the LES zone is essential. Synthetic

turbulence has to be introduced at the RANS-LES interface to ensure a proper bal-

ance between the modeled and the resolved content of turbulence. By such „injec-

tion‟ of resolved turbulence, the balance between RANS and LES turbulence

across the interface is preserved (assuming the synthetic turbulence is of sufficient

quality). Neither DDES nor SAS-type models will be able to switch from RANS

to SRS mode in such situations (e.g. Davidson 2006). Even an explicit switch

12

from a RANS to an LES model (and the corresponding grid refinement) at the in-

terface without an introduction of synthetic turbulence would not work well. If

sufficient resolution is provided in the LES zone, the flow would eventually go

through a transitional process and re-cover the fully turbulent state. However, such

a process would require many boundary layer thicknesses with an entirely unde-

fined model formulation in-between. This is in most technical flows not accepta-

ble and has to be avoided.

The RANS-LES interface should be placed in a non-critical region of the flow

(equilibrium flow), as the synthetic turbulence requires several boundary layer

thicknesses to adjust and become „real‟ turbulence.

As an alternative, the LES simulation can be carried out separately, on a re-

duced domain and by interpolating the „larger‟ RANS solution onto the bounda-

ries of the LES domain. At the inlet of such a domain, again synthetic turbulence

needs to be generated.

The models selected in the RANS and LES zone depend on the flow physics. In

the RANS zone, a suitable model for the flow should be selected. In the LES zone,

the use of a WMLES formulation is typically recommended for wall boundary

layers in order to avoid the unfavorable Reynolds number scaling of classical LES

models. For free shear flows, the WALE (Nicoud and Ducros, 1999), model

should provide good performance.

The following example is a flow through a pipe T-junction with two streams at

different temperatures. This testcase was a used as a benchmark of the OECD to

evaluate CFD capabilities for reactor safety applications. The geometry and grid

are shown in Figure 7. The grid consists of ~5 million hexahedral cells. This flow

is not easily categorized into one of the three groups described above. In principle

it can be computed with SAS and DDES models in SRS mode (not shown). This

means that the instability in the interaction zone between the two streams is suffi-

ciently strong to generate unsteady resolved turbulence. However, it was also ob-

served, that these simulations are extremely sensitive to the details of the numeri-

cal method employed or the shielding function used. The SAS model provided

„proper‟ solutions only when a pure Central Difference scheme was selected, but

went into URANS mode in case of the Bounded Central Difference scheme. The

DDES model provided correct solutions, when a non-conservative shielding func-

tion is used but produces only weak unsteadiness in case of a conservative shield-

ing function. It is therefore recommended to apply the ELES model, where mod-

eled turbulence is converted into synthetic resolved turbulence in both pipes

upstream of the interaction zone at pre-defined RANS-LES interfaces. In addition,

the turbulence model is switched from SST to WMLES at these interfaces. This

then avoids the need for the flow instability of the interacting streams to generate

resolved scales.

13

Figure 7: T-Junction simulation. Upper left: geometry. Upper

right: grid. Lower left: turbulence structures. Lower right: axial

velocity at station X/D=1.6 for horizontal and vertical lines.

Figure 7 (lower left) shows that the resolved turbulence starts already upstream

of the interaction zone due to the introduction of synthetic turbulence. Figure 7

(lower right) shows a comparison of computed and experimental axial velocity

profiles in the main pipe at X/D=1.6. The method provides a good agreement be-

tween the simulations and the experimental data. It can also be seen that the

switch from CD to BCD does not affect the solutions. This is different from the

observation with the SAS model, which reacts sensitive to such changes in the

current testcase.

Summary

An overview of hybrid RANS-LES models in industrial use has been provided.

The main characteristics of the models have been described. It has been argued

that there are three main types of flows, which require different strategies for hy-

brid modelling. Which model to select depends largely on the question, how

strongly the resolved turbulence in the downstream „LES‟ zone depends on the de-

tails of the turbulence in the upstream RANS zone. An attempt was made to define

three different types of flows. In reality, there is clearly a substantial overlap be-

tween the flow types and a characterization is not always easy. However, the cate-

gories should help to conceptually understand which model to apply to which ap-

plication.

14

Acknowledgement

Part of this work was carried out under the EU project ATAAC (Advanced

Turbulence Simulation for Aerodynamic Application Challenges) funded

by the European Community in the 7th Framework Programme under

Contract No. ACP8-GA-2009-233710-ATAAC.

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